Lecture 16

Question 1

What is the macroscopic wavefunction?

Answer 1

The wavefunction that describes all electrons in the superconducting state as they are all in the same quantum eigenstate.

Question 2

Give the equation for the general form of the macroscopic wavefunction

Answer 2

S(r) = phase of the wavefunction
n_p = density of Cooper pairs

Question 3

Give the equation for the density of Cooper pairs

Answer 3

n_p = density of Cooper pairs

Question 4

State the wavefunction of electrons in terms of their momentum

Answer 4

S = phase of the wavefunction
p = momentum of electrons

Question 5

State the London equation

Answer 5

B = magnetic field
λ_L = London penetration depth

Question 6

What is the London equation?

Answer 6

The equation that describes the spatial variation of B within a superconductor.

Question 7

Give the solution to the London equation

Answer 7

B = magnetic field
λ_L = London penetration depth
x = position

Question 8

Give the equation for the critical field of a superconductor in terms of the London penetration depth

Answer 8

B_c = critical field
λ_L = London penetration depth
j_c = critical current density

Question 9

What is the coherence length?

Answer 9

The average distance between electrons in Cooper pairs, based on the energy gap between the electrons at T = 0. It is also the shortest distance of which the Cooper pair density can vary.

Question 10

Describe the graph of electron density and Cooper pair density against distance

Answer 10

Question 11

Describe the graph of the magnetic flux and Cooper pair density against distance for a type I superconductor

Answer 11

Question 12

Describe the graph of the magnetic flux and Cooper pair density against distance for a type II superconductor

Answer 12

Question 13

How does the magnetic energy, the superconducting energy, and the net energy change for a type I superconductor

Answer 13

λ < ζ

Question 14

How does the magnetic energy, the superconducting energy, and the net energy change for a type II superconductor

Answer 14

λ > ζ

Question 15

Describe the flux region of a type I superconductor

Answer 15

Question 16

Describe the flux region of a type II superconductor

Answer 16

Question 17

Describe the shape of a superconductor with dimensions greater than the London penetration depth that has a hole inside

Answer 17

Question 18

Give the equation for Stoke’s theorem

Answer 18

Question 19

Give the equation for the flux through a contour of a superconductor containing a hole

Answer 19

Φ = total flux
n = +/- integer
e = electron charge

Question 20

How does flux pass through a type II superconductor?

Answer 20

It penetrates through very small channels (cores) of a normal conductor.

Question 21

How many flux quanta pass through each core in a type II superconductor?

Answer 21

Exactly one (in the lowest energy state)

Question 22

What gives the superconducting regions in the vortex state of a type II superconductor?

Answer 22

Supercurrents flow around cores, giving B = 0 in superconducting regions.